Definition:Fibonacci Prime Pair

Theorem

A Fibonacci prime pair is a pair of Fibonacci numbers $F_p$ and $F_{p + 2}$ such that:

$p$ and $p + 2$ are both prime numbers

$F_p$ and $F_{p + 2}$ are both prime numbers.

Examples

The only known examples of Fibonacci prime pairs are:

$\tuple {F_5, F_7}, \tuple {F_{11}, F_{13} }, \tuple {F_{431}, F_{433} }, \tuple {F_{569}, F_{571} }$

Sources

• 1988: John Brillhart, Peter L. Montgomery and Robert D. Silverman: Tables of Fibonacci and Lucas Factorizations (Math. Comp. Vol. 50: pp. 251 – 260)  www.jstor.org/stable/2007928

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $5$